Its population may be sparse, but in a seemingly never-ending Democratic primary season, Wyoming for once is claiming its share of high-stakes national attention.

Hillary Clinton and Barack Obama took their fight Friday to the Western state, where caucuses will be held Saturday. The contest in Wyoming offers just 12 delegates. And it's not exactly a blue state -- Republicans have 136,000 registered voters, compared with 59,000 Democrats.

But in this deadlocked Democratic race, every delegate matters, and Wyoming is only the latest state or territory to play an unusually important role in the nominating process.

Clinton's strong showing Tuesday in Ohio, Texas and Rhode Island pushed the race ever forward. After Wyoming this weekend, it heads to Mississippi on Tuesday.

Clinton downplayed expectations Friday, addressing a crowd of more than 1,500 at a community college in Cheyenne.

"I said, 'Well you know what, I'm going to go to Wyoming anyway -- I know it's an uphill climb, I'm aware of that," she said. "But, you see, I am a fighter, and I believe it's worth fighting for your votes."

She set a similar tone while campaigning Thursday night and Friday morning in Mississippi.

However, there haven't been any public polls in Wyoming, so Obama's front-runner status isn't yet backed up by hard numbers.

Both candidates started campaigning personally in the state just this week. Obama talked foreign policy Friday in Casper, Wyo., slamming Clinton's high-profile ad last week that asked voters who they wanted "answering the phone" in a crisis.

"Watch out for this politics of fear," Obama told the crowd. "You know, we're seeing a little bit of it going on right now with this phone call, you know 3 a.m. ... but that was designed to feed into your fears, right?"

He said in such a crisis scenario, he'd exercise the "same judgment" he's shown on Iraq and other foreign policy issues.

Earlier, Obama had stopped by a diner in Casper, where he posed for pictures, shook hands and ordered a burger and vanilla shake.

Wyoming Democratic Party spokesman Bill Luckett said voters are thrilled to play a part -- however fleeting -- in the nominating process.

"It's not a once-every-four-years thing for us," he said. "It's more like a once-every-40-years thing for us."

The last time Wyoming Democrats played a major role was in 1960, when the state's delegation cast 15 votes at the national convention to push Sen. John F. Kennedy over the top, making him the party's nominee for president on the way to defeating Republican Richard Nixon in the general election.

Luckett said several Democratic candidates campaigned in the state in 1988, when it held an early contest. But turnout was low.

He said Wyoming could see turnout Saturday reach about 20 percent, which would be high historically.

"People are super-enthused here," he said. "We have no misconceptions about our place in the order of things. We know it's a real rare thing."

The two Democrats are about 100 delegates apart, and are already girding for a campaign that lasts through Puerto Rico on June 1, and then Montana and South Dakota and June 3.

Bill Clinton made three stops Thursday in Wyoming, talking about clean coal technology and saying there is no rush for the race between his wife and Obama to end.

"Democracy will have its say," he said.

Bill Clinton plans to campaign Saturday in Mississippi.

Neither candidate is willing to cede any ground. Obama blamed his losses Tuesday in part on negative campaigning, and his campaign indicated it would step up the fight.

But that was halted momentarily Friday, as the two candidates traded shots long-distance on their way to Wyoming over comments made by Obama foreign policy adviser Samantha Power.

Power called Clinton a "monster" during an interview with a Scottish newspaper, but after the remarks were published Power apologized and then resigned from Obama's campaign.

The Obama campaign denounced the comments.

FOX News' Aaron Bruns, Bonney Kapp and Judson Berger and The Associated Press contributed to this report.